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Locking and regularization of chimeras by periodic forcing.

Maxim I Bolotov1, Lev A Smirnov1,2, Grigory V Osipov1

  • 1Department of Control Theory, Research and Education Mathematical Center "Mathematics for Future Technologies," Nizhny Novgorod State University, Gagarin Av. 23, 603950, Nizhny Novgorod, Russia.

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External periodic forcing can control chimera states in coupled oscillators. This study reveals how forcing affects chimera states at different scales, leading to frequency entrainment or complex multiplateau dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems

Background:

  • Chimera states, a unique phenomenon in coupled oscillator systems, exhibit coexisting domains of synchronized and desynchronized behavior.
  • Understanding chimera state dynamics is crucial for various fields, including neuroscience and network science.

Purpose of the Study:

  • To investigate the response of one-dimensional chimera states to external periodic forcing.
  • To analyze the effects of forcing on chimera states at macroscopic, mesoscopic, and microscopic levels.

Main Methods:

  • Simulations of nonlocally coupled oscillators subjected to a spatially homogeneous, time-periodic external force.
  • Analysis of system behavior across different scales: macroscopic (frequency entrainment), mesoscopic (pattern regularization), and microscopic (oscillator dynamics).

Main Results:

  • Macroscopic forcing leads to frequency entrainment of the chimera state within an Arnold tongue.
  • Strong forcing can regularize nonstationary chimera patterns at the mesoscopic level.
  • Forcing outside the Arnold tongue induces a multiplateau state with complex locking properties at the microscopic level.

Conclusions:

  • External periodic forcing offers a method to control and modify chimera states in coupled oscillator systems.
  • The response of chimera states to forcing is scale-dependent, revealing rich dynamical behaviors.
  • This study provides insights into the fundamental mechanisms governing complex dynamics in oscillatory networks.